Hadronic Physics I

Geant4 Tutorial at Marshall Space Flight Center

18 April 2012Dennis Wright (SLAC)

Geant4 9.5

Outline

• Overview of hadronic physics• processes, cross sections, models• hadronic framework and organization

• Elastic scattering

• Precompound models• Cascade models• Bertini-style, binary, INCL/ABLA

• Parameterized models• high energy and low energy

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Hadronic Processes, Models and Cross Sections

• In Geant4 physics is assigned to a particle through processes

• Each process may be implemented• directly, as part of the process, or• in terms of a model class

• Geant4 often provides several models for a given process• user must choose• can, and sometimes must, have more than one per process

• A process must also have cross sections assigned• here too, there are options

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process 1at rest

process 1at rest

process 2in-flight

process 2in-flight process 2process 2 process nprocess n

particleparticle

model 1model 2

..

..model n

model 1model 2

..

..model n

c.s. set 1c.s. set 2

……

c.s. set n

c.s. set 1c.s. set 2

……

c.s. set n

Energy range manager

Cross section data store

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Cross Sections

• Default cross section sets are provided for each type of hadronic process• fission, capture, elastic, inelastic• can be overridden or completely replaced

• Different types of cross section sets• some contain only a few numbers to parameterize the c.s.• some represent large databases• some are purely theoretical (equation-driven)

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Alternative Cross Sections

• Low energy neutrons• G4NDL available as Geant4 distribution files• Livermore database (LEND) also available• available with or without thermal cross sections

• Medium energy neutron and proton reaction cross sections• 14 MeV < E < 20 GeV

• Ion-nucleus reaction cross sections• Tripathi, Shen, Kox• good for E/A < 10 GeV

• Pion reaction cross sections

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Cross Section Management

Set 1Set 1

Set 2Set 2

Set 4Set 4

Default cross section setDefault cross section set

Energy

Load

seq

uenc

e

GetCrossSection() sees last set loaded within energy range

GetCrossSection() sees last set loaded within energy range

Set 3Set 3

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Data-driven Hadronic Models• Characterized by lots of data

• cross sections• angular distributions• multiplicities, etc.

• To get interaction length and final state, models depend on interpolation of data• cross sections, Legendre coefficients

• Examples• neutrons (E < 20 MeV)• coherent elastic scattering (pp, np, nn)• radioactive decay

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Theory-driven Hadronic Models• Dominated by theoretical arguments (QCD, Glauber theory,

exciton theory…)

• Final states (number and type of particles and their energy and angular distributions) determined by sampling theoretically calculated distributions

• This type of model is preferred, as it is the most predictive

• Examples•quark-gluon string (projectiles with E > 20 GeV)•intra-nuclear cascade (intermediate energies)•nuclear de-excitation and break-up

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Parameterized Hadronic Models• Depend mostly on fits to data with some theoretical guidance

• Two such models available:•Low Energy Parameterized (LEP) for E < 20 GeV•High Energy Parameterized (HEP) for E > 20 GeV•each type refers to a collection of models (one for each hadron type)

• Both LEP and HEP are re-engineered versions of the Fortran Gheisha code used in Geant3

• Code is fast and applies to all particle types, but is not particularly detailed •eventually will be phased out

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Partial Hadronic Model Inventory

Bertini-style cascadeBertini-style cascade

Binary cascadeBinary cascade

1 MeV 10 MeV 100 MeV 1 GeV 10 GeV 100 GeV 1TeV

Fermi breakupFermi breakup

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At rest absorption, , , K, anti-p

At rest absorption, , , K, anti-p

High precision neutron

High precision neutron

EvaporationEvaporation

MultifragmentMultifragmentPhoton EvapPhoton Evap

Pre-compound

Pre-compound

Radioactive decay

Radioactive decay

Fritiof stringFritiof string

Quark Gluon stringQuark Gluon string

Photo-nuclear, electro-nuclearPhoto-nuclear, electro-nuclear

QMD (ion-ion)QMD (ion-ion)

Electro-nuclear dissociationElectro-nuclear dissociation

Wilson AbrasionWilson Abrasion

Model Management

Model 1Model 1 Model 2Model 2

Model 4Model 4

Energy

Model returned by GetHadronicInteraction()Model returned by GetHadronicInteraction()

Model 3Model 3

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11 1 + 31 + 3 33 ErrorError 22 ErrorError 22

at restat rest discrete (in-flight)discrete (in-flight)

modelsmodels

processprocess

theory frameworktheory framework

high energyhigh energy spallation frameworkspallation framework

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Hadronic Model Organization

cascadecascadeprecompoundprecompound

evaporationevaporation

parton-stringparton-string propagatepropagate

string fragmentationstring fragmentation

Hadronic Interactions from TeV to meV

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dE/dx ~ A1/3 GeV

TeV hadron

~GeV to ~100 MeV

~100 MeV to ~10 MeV

p, n, d, t,

~10 MeV to thermal

and n

Hadron Elastic Scattering

• G4WHadronElasticProcess: general elastic scattering • valid for all energies• valid for p, n, , K, hyperons, anti-nucleons, anti-hyperons• based in part on old Gheisha code, but with relativistic

corrections• Coherent elastic

• G4LEpp for (p,p), (n,n) : taken from SAID phase shift analysis, good up to 1.2 GeV

• G4LEnp for (n,p) : same as above• G4HadronElastic for general hadron-nucleus scattering

• Neutron elastic• high precision (HP) model uses data from ENDF (E < 20 MeV)

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Elastic Scattering Validation(G4HadronElastic)

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Precompound Models

• G4PrecompoundModel is used for nucleon-nucleus interactions at low energy and as a nuclear de-excitation model within higher-energy codes • valid for incident p, n from 0 to 170 MeV• takes a nucleus from a highly excited set of particle-hole states

down to equilibrium energy by emitting p, n, d, t, 3He and • once equilibrium is reached, four other models are called to

take care of nuclear evaporation and break-up• these 4 models not currently callable by users

• The parameterized models and two cascade models have their own version of nuclear de-excitation models embedded in them

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Precompound Models• Invocation of Precompound model: G4ExcitationHandler* handler = new G4ExcitationHandler; G4PrecompoundModel* preco = new G4PrecompoundModel(handler); // Create de-excitation models and assign them to precompound model G4NeutronInelasticProcess* nproc = new G4NeutronInelasticProcess; nproc->RegisterMe(preco); neutronManager->AddDiscreteProcess(nproc); // Register model to process, process to particle

• Here the model is invoked in isolation, but usually it is used in combination with high energy or cascade models• a standard interface exists for this

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Bertini-style Cascade Model

• A classical (non-quantum mechanical) cascade• average solution of a particle traveling through a medium

(Boltzmann equation)• no scattering matrix calculated• can be traced back to some of the earliest codes (1960s)

• Core code:• elementary particle collisions with individual protons and

neutrons: free space cross sections used to generate secondaries

• cascade in nuclear medium• pre-equilibrium and equilibrium decay of residual nucleus• target nucleus built of three concentric shells

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Bertini Cascade ( 0 < E < 10 GeV)

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1 to 3 uniform density shells

p, n, d, t,

and n

Using the Bertini Cascade

• In Geant4 the Bertini cascade is used for p, n, +, -, K+, K-, K0L ,

K0S, , 0 , + , - , 0 , -

• valid for incident energies of 0 – 10 GeV• soon to be extended for use with gammas

• Invocation sequence G4CascadeInterface* bert = new G4CascadeInterface; G4ProtonInelasticProcess* pproc = new G4ProtonInelasticProcess; pproc->RegisterMe(bert); protonManager->AddDiscreteProcess(pproc);// same sequence for all other hadrons

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Validation of Bertini Cascade

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Binary Cascade Model

• Modeling sequence similar to Bertini, except• it’s a time-dependent model• hadron-nucleon collisions handled by forming resonances which

then decay according to their quantum numbers • particles follow curved trajectories in smooth nuclear potential

• Binary cascade is currently used for incident p, n and • valid for incident p, n from 0 to 10 GeV• valid for incident + , – from 0 to 1.3 GeV

• A variant of the model, G4BinaryLightIonReaction, is valid for incident ions up to A = 12 (or higher if target has A < 12)

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Using the Binary Cascade• Invocation sequence: G4BinaryCascade* binary = new G4BinaryCascade(); G4PionPlusInelasticProcess* piproc = new G4PionPlusInelasticProcess(); piproc->RegisterMe(binary); piplus_Manager->AddDiscreteProcess(piproc);

• Invoking BinaryLightIonReaction G4BinaryLightIonReaction* ionBinary =

new G4BinaryLightIonReaction();

G4IonInelasticProcess* ionProc = new G4IonInelasticProcess();

ionProc->RegisterMe(ionBinary);

genericIonManager->AddDiscreteProcess(ionProc);24

Validation of Binary Cascade256 MeV protons

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INCL Cascade Model

• Model elements• time-dependent model• smooth Woods-Saxon or harmonic oscillator potential• particles travel in straight lines through potential• delta resonance formation and decay (like Binary cascade)

• Valid for incident p, n and d, t, 3Hefrom 150 MeV to 3 GeV• also works for projectiles up to A = 12• targets must be 11 < A < 239• ablation model (ABLA) can be used to de-excite nucleus

• Used successfully in spallation studies• also expected to be good in medical applications

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Validation of INCL ModelGreen: INCL4.3 Red: INCL4.2 Blue: Binary cascade

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LEP, HEP Models

• Formerly known as Gheisha and used in Geant3• not very detailed, but very fast• valid for all long-lived hadrons• LEP up to 30 GeV, HEP above 20 GeV

• Very simple model• no nuclear model, only Z and A required• a hadron interacts with a random nucleon• in the CM frame all reaction products divided in forward and

backward clusters• clusters are then fragmented into hadrons• remnant nucleus de-excited by emission of p, n, d, t,

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LEP, HEP Models (all energies)

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nucleus not modeled

CM frame and n

Using the LEP and HEP Models

• Invocation sequence: G4ProtonInelasticProcess* pproc = new G4ProtonInelasticProcess; G4LEProtonInelastic* LEproModel = new G4LEProtonInelastic; pproc->RegisterMe(LEproModel); G4HEProtonInelastic* HEproModel =new G4HEProtonInelastic; HEproModel->SetMinEnergy(25*GeV); pproc->RegsiterMe(HEproModel); proton_manager->AddDiscreteProcess(pproc);

• Note: • on an event-by-event basis, these models do not conserve

energy• average shower distributions, however, are good

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Summary (1)

• Geant4 hadronic physics allows user to choose how a physics process should be implemented• cross sections• models

• Many processes, models and cross sections to choose from• hadronic framework makes it easier for users to add more

• General hadron elastic scattering handled by G4WHadronElasticProcess

• Precompound models are available for low energy nucleon projectiles and nuclear de-excitation

ConstructGeneral(); // method may be defined by user to hold all other processes

}

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Summary (2)

• Three intra-nuclear cascade models available to cover medium energies (up to 10 GeV)• Bertini-style• Binary cascade• INCL

• Parameterized models (LEP, HEP) handle the most particle types over the largest energy range• based on fits to data and a little bit of theory• not very detailed and do not conserve energy• fast• being slowly phased out

ConstructGeneral(); // method may be defined by user to hold all other processes

}

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